Least Common Multiple (LCM) of 23 and 102
The least common multiple (LCM) of 23 and 102 is 2346.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 23 and 102?
First, calculate the GCD of 23 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 23 ÷ 102 = 0 remainder 23 |
| 2 | 102 ÷ 23 = 4 remainder 10 |
| 3 | 23 ÷ 10 = 2 remainder 3 |
| 4 | 10 ÷ 3 = 3 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 65 and 132 | 8580 |
| 16 and 80 | 80 |
| 141 and 86 | 12126 |
| 168 and 191 | 32088 |
| 189 and 151 | 28539 |